The sum of three consecutive integers is 267. If the first one is a, then the second would be a + 1, while the third would be a + 2. Therefore, you would have;
[tex]\begin{gathered} a+(a+1)+(a+2)=267 \\ a+a+1+a+2=267 \\ 3a+3=267 \\ \text{Subtract 3 from both sides} \\ 3a=264 \\ \text{Divide both sides by 3} \\ a=88 \end{gathered}[/tex]The largest (third) integer is a + 2, therefore
[tex]\begin{gathered} a+2=88+2 \\ a+2=90 \end{gathered}[/tex]The largest integer therefore is 90.
